Brake system control

ABSTRACT

A brake system control method, comprising the steps of: measuring a set of vehicle parameters including steering wheel angle, vehicle speed, lateral acceleration and vehicle yaw rate; responsive to the measured parameters using an observer to estimate lateral velocity of the vehicle, wherein the observer contains (a) an open loop dynamic model of the vehicle responsive to the measured vehicle speed and the measured yaw rate, (b) a closed loop term responsive to a first error between the measured yaw rate and a predicted yaw rate, a second error between a previously estimated lateral velocity and a predicted lateral velocity and a third error between the measured lateral acceleration and a predicted lateral acceleration; estimating a vehicle slip angle responsive to the estimate of lateral velocity; determining a control command responsive to the vehicle slip angle; and controlling an actuator responsive to the control command.

This invention relates to a brake system control.

BACKGROUND OF THE INVENTION

Automotive vehicles have been produced or demonstrated with brakesystems that modulate brake force during stops to provide anti-lockbrake control (ABS) and/or that modulate brake force during vehicleacceleration to provide positive acceleration traction control (TCS).Some such brake systems additionally provide brake-by-wire control.

More recently, vehicles have been produced with brake systems thatactivate in certain situations where some or all vehicle tires areexperiencing excessive lateral movement relative to the road surface.The brakes are selectively controlled to attempt to bring the vehicle toa desired course and/or to minimize the lateral movement of the tiresrelative to the road surface.

SUMMARY OF THE INVENTION

It is an object of this invention to provide a brake system controlmethod according to claim 1.

Advantageously this invention provides a brake system control method foractively controlling the road response of a motor vehicle.

Advantageously this invention provides a brake system control method andapparatus that provides a control of vehicle slip angle, for example, byselectively activating vehicle wheel brakes to reduce a differencebetween actual vehicle slip angle and a desired vehicle slip angle.

Though vehicle slip angle is difficult to measure directly, an advantageprovided by this invention includes a dynamic observer for estimatingvehicle slip angle. Advantageously the dynamic observer is iterative,providing estimations of vehicle slip angle, vehicle lateral velocity,tire slip angles and lateral forces of the front and rear axles. Eachmost recent estimation of lateral velocity is used as an input alongwith vehicle speed and measured vehicle yaw rate to estimate side slipangles of the front and rear tires. The tire side slip angles are thedifferences between the rolling direction (non lateral) and actualdirection of the vehicle tires. The estimated tire side slip angles areused with the estimated lateral coefficient of adhesion between thevehicle tires and the road surface to estimate lateral tire forces. Amodel within the observer uses the estimated lateral tire forces,lateral acceleration of the vehicle, yaw rate of the vehicle and vehiclespeed to estimate the next iteration of vehicle lateral velocity andvehicle side slip angle.

Advantageously, the observer balances the reliability of the model withfeedback from sensor measurements, provides estimates in both linear andnonlinear ranges of handling behavior on various coefficient of adhesionsurfaces and includes compensation for the errors caused by bank angleof the road.

Advantageously, according to one example, this invention provides abrake system control method, comprising the steps of: measuring a set ofvehicle parameters including steering wheel angle, vehicle speed,lateral acceleration and vehicle yaw rate; responsive to the measuredparameters using an observer to estimate lateral velocity of thevehicle, wherein the observer contains (a) an open loop dynamic model ofthe vehicle responsive to the measured vehicle speed and the measuredyaw rate, (b) a closed loop term responsive to a first error between themeasured yaw rate and a predicted yaw rate, a second error between apreviously estimated derivative of lateral velocity and a predictedderivative of lateral velocity and a third error between the measuredlateral acceleration and a predicted lateral acceleration; estimating avehicle slip angle responsive to the estimate of lateral velocity;determining a control command responsive to the vehicle slip angle; andcontrolling an actuator responsive to the control command.

Advantageously, according to another example, this invention provides abrake system control method comprising the steps of: estimating a frontside slip angle of front vehicle wheels; estimating a rear side slipangle of rear vehicle wheels; estimating a first lateral force of thefront wheels on a road surface responsive to the first side slip angle;estimating a second lateral force of the rear wheels on the road surfaceresponsive to the second side slip angle; wherein the first lateralforce estimation is responsive to a first function for low values of thefront side slip angle and responsive to a second function for highvalues of the front side slip angle; wherein the second lateral forceestimation is responsive to a third function for low values of the rearside slip angle and responsive to a fourth function for high values ofthe rear side slip angle; estimating a vehicle lateral velocityresponsive to the first and second lateral force estimation; estimatinga vehicle slip angle responsive to the vehicle lateral velocity and avehicle forward velocity; determining a control command responsive tothe estimated vehicle slip angle; and controlling a chassis systemactuator responsive to the control command.

According to a preferred example, the first lateral force estimation isresponsive to the first function when a first product of the first sideslip angle and an estimate of surface coefficient of adhesion is below afirst threshold and responsive to the second function when the firstproduct is not below the first threshold, and the second lateral forceestimation is responsive to the second function when a second product ofthe second side slip angle and the estimate of surface coefficient ofadhesion is below a second threshold and responsive to the fourthfunction when the second product is not below the second threshold.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described by way of example withreference to the following drawings, in which:

FIG. 1 is an example schematic of a vehicle brake control systemaccording to this invention;

FIG. 2 illustrates an example diagram of vehicle dynamics according tothis invention;

FIG. 3 illustrates an example control according to this invention;

FIG. 4 illustrates an example vehicle slip angle observer according tothis invention;

FIGS. 5-7 illustrate example gain functions for use with the examplesystem described below;

FIGS. 8-12 illustrate command flow diagrams of example control functionsaccording to this invention;

FIG. 13 illustrates an example vehicle reference model;

FIG. 14 illustrates another example vehicle reference model; and

FIG. 15 illustrates an example tire force function.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIG. 1, the vehicle 10 shown includes a controllable brakesystem with controller 68 for controlling the brakes 20, 22, 24 and 26of the vehicle wheels 12, 14, 16 and 18, respectively. Various inputs tothe controller 68 include the wheel speed signals on lines 36, 38, 40and 42 from wheel speed sensors 28, 30, 32 and 34, the brake pedalswitch signal on line 84 from brake pedal switch 82, the brake pedalextended travel signal on line 83 from pedal travel sensor 85(optional), the steering wheel angle signal on line 62 from sensor 61indicating the angle of steering wheel 60, the yaw rate signal on line81 from yaw rate sensor 80, the master cylinder pressure signal on line96 from master cylinder pressure sensor 94 (optional) and the lateralacceleration signal on line 99 from lateral accelerometer 98.

Each of the sensors 28, 30, 32, 34, 61, 80, 82, 85, 94 and 98 isimplemented in a manner known to those skilled in the art. The brakepedal travel sensor 85 is a switch mounted to the pedal that provides anoutput signal when the pedal has been depressed an extended amountindicating “hard” braking by the driver.

In one example, the steering wheel position sensor 61 may be a digitalsensor that provides output signals that increment a digital positionsignal within controller 68 with each degree or partial degree ofmovement of the steering wheel 60 in one direction and decrement thedigital position signal with each degree or partial degree of movementin the opposite direction. The steering wheel sensor 61 may also includean analog sensor position output (i.e., from a rotary resistive deviceof a known type) that provides approximate steering wheel positioninformation. The analog output can be used, for example, to determinewhether the steering wheel is turned less than a preset limit, i.e., 90degrees, at vehicle start-up. A method for determining the centerposition of the steering wheel position sensor is disclosed in pendingU.S. patent application, Ser. No. 08/664,321, assigned to the assigneeof this invention.

Responsive to the various inputs, the controller controls the braking ofeach wheel in anti-lock braking mode during certain braking maneuversand in traction control mode during certain vehicle accelerationmaneuvers to maintain tractive force of the drive wheels on the roadsurface. The anti-lock brake control and positive acceleration tractioncontrol are performed in a known manner except as modified herein.

The controller 68 also actively controls the wheel brakes 20, 22 (in atwo channel system) or 20, 22, 24 and 26 (in a four channel system)responsive to the actual vehicle yaw rate and actual vehicle lateralacceleration as measured by sensors 80 and 98, respectively, to minimizethe difference between the actual vehicle yaw rate and a desired vehicleyaw rate and to minimize the difference between the actual vehicle slipangle and the desired vehicle slip angle. Because the base braking,antilock braking and traction control functions are known to thoseskilled in the art, only a general description thereof will be set forthherein.

When the vehicle is in a braking maneuver, the controller monitors thewheel speed signals from sensors 28, 30, 32 and 34 and determines if oneor more of the wheels is in or is about to be in an incipient lock-upcondition, in which case anti-lock brake control mode for the one ormore wheels is activated. In the anti-lock brake control mode, thecontroller 68 determines and outputs commands to the actuators 52, 54,56 and 58 corresponding to the wheels in anti-lock brake mode tomodulate brake force to the wheels. Through control of the actuators 52,54, 56 and 58, the controller prevents the wheels from entering alock-up condition while achieving effective brake control andsteeribility in a manner known to those skilled in the art of anti-lockbrake control.

When the vehicle is not in a braking maneuver, but is accelerating dueto output motive force from the vehicle prime mover, i.e., the internalcombustion engine or electric motor, the controller 68 monitors thewheel speeds sensed by sensors 28, 30, 32 and 34 to determine if thewheels transferring motive force to the road surface are slipping or areabout to slip. In such wheel conditions, the controller 68 sendscommands to the actuators 52-58 corresponding to the wheels that areslipping or are about to slip to provide brake force to the wheels toreduce the slip. Such control is typically performed in conjunction witha parallel control in the engine or motor (and/or the transmission)controller to temporarily reduce the motive force output untilwheel-to-road traction is reestablished.

In one example, the brake actuators 52-58 are implemented asreciprocating piston actuators of a type known to those skilled in theart. Such actuators typically include a dc motor positionallycontrolling a reciprocating piston through a rotary-to-linear motionconverter to increase and/or decrease hydraulic pressure in the wheelbrakes. In another example, brake actuators 52-58 are implemented assolenoid valves for selectively coupling brakes 20-26 to a source ofpressurized hydraulic fluid to increase brake pressure and forselectively coupling brakes 20-26 to a brake fluid reservoir to decreasebrake pressure. Implementation of such solenoid valves is known to thoseskilled in the art. In yet another example, the rear brakes and/or thefront brakes may be electric motor-driven brakes, in which case theactuator and brake functions are performed by the same unit. An exampleof a brake system including front hydraulic brakes and rear electricbrakes in which all four brakes are controlled in a brake-by-wire methodis set forth in U.S. Pat. No. 5,366,291, assigned to the assignee ofthis invention.

The example system describe herein performs an active brake control ofthe two wheel brakes 20 and 22 or of the four wheel brakes 20, 22, 24and 26 responsive to the steering wheel angle signal on line 62, the yawrate signal on line 81, the vehicle speed as calculated responsive tothe signals from the four wheel speed sensors, the lateral accelerationsignal on line 99 and either the brake pedal extended travel sensor 85or the master cylinder pressure sensor 94. Using these signals,controller 68 determines a desired vehicle yaw rate and compares thatdesired yaw rate to the actual yaw rate sensed by sensor 80. Thecontroller 68 also determines a desired vehicle slip angle (definedbelow) and compares that desired vehicle slip angle to the actualvehicle slip angle as determined by an estimator or observer in thecontroller. If the yaw rate of the vehicle differs from the desired yawrate by more than a yaw rate threshold that is dynamically determined,or if a desired corrective yaw moment determined responsive to yaw rateerror and slip angle error is greater than a yaw moment threshold,controller 68 determines and outputs commands to actuators 52, 54, 56and 58 to control the vehicle wheel brakes 20, 22, 24 and/or 26 to bringthe vehicle yaw rate and slip angle into conformance with the desiredyaw rate and slip angle. In a two channel system, only brakes 20 and.22are controlled via actuators 52 and 54, respectively.

In carrying out these tasks, controller 68 typically includes amicroprocessor, ROM and RAM and appropriate input and output circuits ofa known type for receiving the various input signals and for outputtingthe various control commands to the actuators 52, 54, 56 and 58.

Referring now to FIG. 2, the schematic diagram illustrates the conceptsof slip angle and yaw rate control. The vehicle 10 has a longitudinalaxis 201 oriented in what is referred to as the x direction or theforward direction of the vehicle. The vector denoted by reference 204illustrates an example true velocity of the vehicle center of gravity,which has a direction oriented at an angle A, denoted by reference 202,from the x axis or longitudinal axis 201 of the vehicle. The vector 204has longitudinal (x axis) velocity component 208 and lateral velocitycomponent 206, which is parallel to what is referred to herein as the yaxis. Reference 200 represents the vehicle center of gravity.

During vehicle maneuvering operations, there are generally two kinds ofvehicle behavior. The first is linear behavior during which thevehicle's yaw rate and slip angle have fixed relationships to steeringwheel angle and vehicle forward velocity. A nonlinear operation of thevehicle is characterized by significant lateral movement of at leastsome of the vehicle tires with respect to the road surface. Duringnonlinear operation, the vehicle's yaw rate 210 and slip angle 202deviate from the fixed relationships to steering wheel angle and vehicleforward velocity that are characteristic of linear operation.

This invention advantageously reduces the deviation of the vehicle's yawrate 210 and slip angle 202 from desired yaw rates and slip anglesduring many nonlinear operating conditions of the vehicle. The controlof the vehicle yaw rate and slip angle is achieved by the selectiveapplication of brake forces at the vehicle wheels 12, 14 (in a twochannel system) or 12, 14, 16 and 18 (in the four channel system) toinduce yaw moments on the vehicle 10 countering the undesirable yawmovement detected of the vehicle 10. These brake forces are illustratedgraphically by references 212. Additionally, during braking maneuvers ayaw moment may be introduced by decreasing brake forces at select wheelswhile maintaining or increasing the brake forces at other wheels.Decreases in brake forces are represented by references 214. Thus, it isthrough the selective increase and/or decrease of brake forces at thevehicle wheels 12, 14 (two channel system) or 12, 14, 16 and 18 (fourchannel system) that yaw moments are induced on the vehicle 10 tominimize the respective differences between desired and actual yaw ratesand between desired and actual slip angles.

Referring now to FIG. 3, the example control shown includes the vehiclereference model 102, block 104 representing the vehicle, estimators 120and 122 for estimating the actual surface coefficient of adhesion andvehicle slip angle, respectively, yaw command and slip command controlblocks 138, 142, output command block 154 and the brake actuators andwheel brakes represented by blocks 132 and 128, respectively.

In the following sections, time values denoted with a (k) representpresent control-loop values and time values denoted by (k−n) representthe nth most recent control-loop values in a conventional manner. Wheretime value denotations, i.e., (k), are omitted from equations, it isassumed that the time value denotation is (k) unless otherwisespecified.

The vehicle reference model receives inputs from lines 112, 62 and 121representing the vehicle forward velocity, steering wheel angle andestimated surface coefficient of adhesion. The vehicle reference modeluses the inputs to calculate desired vehicle slip angle, desired vehiclelateral velocity and desired vehicle yaw rate according to the followingequations:

v _(yd)(k)=(1+a ₁₁ *Δt)*v _(yd)(k−1)+a ₁₂ *Δt*Ω _(du)(k−1)+b ₁*Δt*δ(k−1),

 Ω_(du)(k)=a ₂₁ *Δt*v _(yd)(k−1)+(1+a ₂₂ *Δt)*Ω_(du)(k−1)+b ₂*Δt*δ(k−1),

and

β_(du)=Arctan(v _(yd) /v _(x)),

where Δt is the sampling period (control loop time) and

a ₁₁=−(c _(f) +c _(r))/(M*v _(x)), a ₁₂=(−c _(f) *a+c _(r) *b)/(M*v_(x))−v _(x),

a ₂₁=(−c _(f) *a+c _(r) *b)/(I _(zz) *v _(x)), a ₂₂=−(c _(f) *a ² +c_(r) *b ²)/(I _(zz) *v _(x)),

b ₁ =c _(f) /M and b ₂ =a*c _(f) /I _(zz),

where δ is the steering angle of the front wheels, M is the total massof the vehicle, I_(zz) is the moment of inertia of the vehicle about theyaw axis (passing through the center of gravity), a and b are distancesfrom the center of gravity of the vehicle to the front and rear axles,c_(f) and c_(r) are cornering stiffness coefficients of both tires offront and rear axles, respectively, v_(x) is the forward velocity of thevehicle, v_(yd)(k) is the desired lateral velocity of the vehicle attime k, Ω_(du)(k) is the desired yaw rate (unlimited) of the vehicle attime k and β_(du) is the unlimited desired slip angle of the vehicle.

It is noted that the above vehicle model is a preferred example andother vehicle models may be used as alternatives to determining thedesired vehicle yaw rate and slip angles.

The reference model 102 then limits the desired values of slip angle andyaw rate, where the maximum value of the desired slip angle isdetermined responsive to the estimated surface coefficient of adhesionμ_(e) determined at block 120 and output on line 121. Typically, road totire surface coefficient of adhesions are in the range of 0.2 to 1.0;0.2 representing ice and 1.0 representing dry pavement. The maximumdesired slip angle will be predetermined by the vehicle designer and mayvary from vehicle type to vehicle type. In one example, the maximumdesired slip angle on ice is 4° of slip angle and on a dry surface is10°. Assuming these parameters, then the maximum desired slip angle,β_(max), is determined as follows:$\beta_{\max \quad t} = \left\{ {{\begin{matrix}{10*{\pi/180}} & {{{when}\quad \mu_{e}} \geq 1.0} \\{\left( {{7.5*\mu_{e}} + 2.5} \right){\pi/180}} & {{{when}\quad 0.2} < \mu_{e} < 1.0} \\{4*{\pi/180}} & {{{when}\quad \mu_{e}} \leq 0.2}\end{matrix}{and}\beta_{\max \quad t}} = \left\{ \begin{matrix}{\max \left( {\beta_{\max \quad t},{\beta_{du}}} \right)} & {{{if}\quad \beta_{du}*\delta} \geq 0.005} \\\beta_{\max} & {otherwise}\end{matrix} \right.} \right.$

The condition β_(du)*δ≧0.005 may be replaced by the conditionv_(x)<[c_(r)*b*(a+b)/(M*a)]^(½) since, when this condition is met, thesigns of β_(du) and δ are the same. Once β_(max) is determined, thedesired slip angle is limited according to the following equation:$\beta_{d} = \left\{ \begin{matrix}\beta_{du} & {{{when}\quad {\beta_{du}}} \leq \beta_{\max}} \\{\beta_{\max}*\left( {{\beta_{du}}/\beta_{du}} \right)} & {{{when}\quad {\beta_{du}}} > \beta_{\max}}\end{matrix} \right.$

According to the above equations, β_(d) is not limited when the signs ofslip angle and steering angle are the same, or equivalently when vehiclespeed is below the value defined above.

The desired yaw rate, Ω_(d), is determined as Ω_(du), limited to plusand minus a predetermined parameter set, for example equal to 0.2 or 0.3radians per second above the maximum yaw rate sustainable by the vehicleon a dry (high coefficient of adhesion) surface. The limit on thedesired yaw rate may be speed dependent (e.g., the maximum magnitude forΩ_(d) may be limited to a_(ymax)/v_(x)+0.3).

The desired lateral acceleration, a_(yd), is determined as:

 a _(yd) =v _(yd) ′+v _(x) *Ω _(du),

where v_(yd)′ is the time derivative of v_(yd) and may be computed as:

a ₁₁ *v _(yd) +a ₁₂*Ω_(du) +b ₁*δ

or as

(v _(yd)(k)−v _(yd)(k−1))/Δt.

The reference model 102 outputs the desired slip angle, β_(d), on line106, the desired yaw rate, Ω_(d), on line 108 and the desired lateralacceleration, a_(yd), on line 110.

The desired lateral acceleration on line 110 and the actual vehiclelateral acceleration on line 99, are provided to block 120 along withthe measured vehicle yaw rate, Ω_(a), on line 81, desired yaw rate,Ω_(d), steering angle, δ, and vehicle speed, v_(x). Block 120 uses theactual and desired lateral accelerations and the actual and desiredvehicle yaw rates to estimate a coefficient of adhesion between the roadsurface and the vehicle tires.

Before measured lateral acceleration is used in the algorithm, it ismultiplied by a roll factor, r_(fac), in order to reduce the effect ofvehicle roll during turning maneuvers on the measured lateralacceleration. The roll factor may be computed as:

r _(fac)=1/(1+M*g*h/φ),

where h is the height of the vehicle center of gravity and φ is thetotal roll stiffness of the vehicle suspension. For a typical sedan,r_(fac)≈0.9. From this point on, the term measured lateral acceleration,a_(y), refers to the lateral acceleration measured by the sensor 98,multiplied by r_(fac) and filtered through a low pass filter, e.g., asecond order Butterworth filter having a cut off at 40 rad/s to reducenoise from the sensor signal.

The estimation at block 120 first uses the steering angle and vehiclevelocity to compute a value, Ω_(dss), referred to as the desired yawrate at steady state, as follows:

Ω_(dss) =v _(x)*δ/((a*b)+K _(u) *v _(x) ²),

where K_(u) is the vehicle understeer coefficient, defined as:

K _(u)=(c _(r) *b−c _(f) *a)*M/(c _(f) *c _(r)*(a+b)).

The value Ω_(dss) differs from Ω_(d) in that it does not account for thedynamic delay in the vehicle model that is included in the calculationof Ω_(d). The measured and desired lateral accelerations are passedthrough identical low pass filters to attenuate noise in the measuredlateral acceleration signal. The desired lateral acceleration is thenfiltered through another low pass filter, for example, a standard secondorder Butterworth filter with a cut off frequency of 22 radians persecond in order to reduce (or eliminate) the phase difference betweenthe two signals. Then a value, a_(ydfl), is determined by limiting theoutput of the Butterworth filter to +/−a_(ymax), where a_(ymax) is themaximum lateral acceleration that the vehicle can sustain on a drysurface. The magnitude of the lateral acceleration error, Δ_(ay), isthen determined according to:

Δa _(y) =|a _(ydfl) −a _(y)|,

where a_(y) denotes the measured and filtered lateral acceleration. Thevalue Δa_(y) is then filtered through a first order digital low passfilter, for example, with a cut off frequency of 2 radians per second,to yield the filtered lateral acceleration error, Δa_(yf).

A preliminary estimate of lateral surface coefficient of adhesion,μ_(ay), is determined according to:

μ_(ay) =|a _(y) |/a _(ymax).

Then a value μ_(temp) is determined equal to μ_(ay) if all of thefollowing conditions are met simultaneously:

|a _(ydfl) |−|a _(y)|>THRESH1;  (a)

|Ω_(dss)−Ω_(a)|>THRESH2;  (b)

and (c) the signs of the desired and actual lateral accelerations arethe same and have been the same for at least a specified period of time,e.g., 0.3 seconds.

In condition (b) above, Ω_(d) could be used instead of Ω_(dss), butΩ_(dss) is preferable because the yaw rate error developed from|Ω_(dss)−Ω_(da)| is more likely to be in phase with lateral accelerationerror than |Ω_(d)−Ω_(a)|.

In the condition (c) above, the time that desired and actual lateralaccelerations have opposite signs is tracked, for example, with a timerTi, defined as: ${Ti} = \left\{ \begin{matrix}{{0\quad {if}\quad a_{ydfl}*a_{y}} < {{- 0.1}\quad {or}\quad a_{y\quad d}*a_{y}} < {- 0.1}} \\{{{Ti} + {\Delta \quad t}},{otherwise}}\end{matrix} \right.$

where a_(yd) is the desired (unfiltered) lateral acceleration, Δt is theloop time of the control algorithm and 0.1 is an example constant to bedetermined as appropriate by the system designer. Condition (c) is metwhen Ti>0.3 seconds.

Also μ_(temp) is set equal to μ_(ay) if the following three conditionsare met simultaneously: (a) the vehicle velocity is small, for example,below 7 meters/second; (b) the signs of a_(ydfl) and a_(y) are the sameand have been the same for at least a specified period of time, e.g.,0.3 seconds; and

|Ω_(d)−Ω_(a)|>THRESH3,  (c)

where THRESH1, THRESH2 and THRESH3 are predetermined threshold valuescorresponding to lateral acceleration error and two yaw rate errors whenthe vehicle's behavior begins to deviate significantly from that of thelinear model (i.e., the vehicle enters a non-linear range of operation).Example values for THRESH 1, THRESH2 and THRESH3 are 1.2 m/s², 0.10rad/s and 0.14 rad/s, respectively. These threshold values may be madespeed dependent. Also the value μ_(temp) is set equal to μ_(ay),regardless of the above conditions, if the following condition is met:

|a _(y) |a _(ymax)>1.05*μ_(temp).

This above condition corrects the surface estimate when the magnitudesof measured lateral acceleration rises at least a given percentage(e.g., 5%) above the value that the present surface estimate wouldpermit (μ_(temp)*a_(ymax)).

The reset value for μ_(temp) is 1.0 and μ_(temp) is reset to 1.0 whenthe following conditions are simultaneously met:

|a _(ydfl) −a _(y)|≦THRESH1,  (a)

Δa _(yf)<0.5*THRESH1,  (b)

 |Ω_(d)−Ω_(a)|<THRESH3,  (c)

and the a_(yd), a_(ydfl) and a_(y) have the same sign and have had thesame sign for at least a specified time period, e.g., Ti>0.3 s.

If neither the set of criteria indicating linear operation nor the setof conditions triggering calculation of surface estimate from lateralacceleration are met, then the estimate μ_(temp) is maintained at itsmost recent estimated value, i.e., μ_(temp)(k)=μ_(temp)(k−1).

A value μ_(new) is determined according to:

μ_(new)=(0.85+0.15*μ_(temp))*μ_(temp),

where the parameters 0.85 and 0.15 may vary for different types ofvehicles. The value μ_(new) is then limited to no less than 0.07 and nogreater than 1.0 to get μ_(L), which is output on line 123 as theestimated surface coefficient of adhesion used in the slip angleestimation block 122. The estimated surface coefficient of adhesion usedfor the control blocks 138 and 142 and used in the vehicle referencemodel 102 is determined by passing μ_(new) through a low pass filter,for example a second order Butterworth filter having a cut off frequencyof 1.5 Hz. The filter output is then limited to no less than 0.2 and nogreater than 1.0 to determine μ_(e), the signal on line 121.

Block 122 estimates the side slip angle of the vehicle with a nonlineardynamic observer. The observer 122 implements a vehicle model driven bytwo types of inputs: the steering input used by the driver to controlthe vehicle and the error signals, which are the differences between themeasured (feedback) signals, lateral acceleration and yaw rate, andestimations predicted by the model. The feedback terms providecorrection when the estimates deviate from actual measured values,preventing the tendency of the estimates to diverge with time because ofinaccuracies between the model and the actual system and because ofexternal disturbances.

Since the dynamic response of the vehicle at or close to the limit ofadhesion depends strongly on the surface coefficient of adhesion, theobserver 122 for estimating the vehicle slip angle relies on theestimated coefficient of adhesion determined at block 120 FIG. 3.

Assuming a small steering angle, δ, dynamics of a bicycle vehicle modelin a horizontal plane can be described by the following equations (inthe following equations d/dt denotes time derivatives):

dv _(y) /dt=−v _(x)*Ω+(F _(yf) +F _(yr))/M

dΩ/dt=(a*F _(yf) −b*F _(yr))/I _(zz)

where v_(y) is the lateral velocity and F_(yf) and F_(yr) are thelateral forces of the front and rear axles, respectively. Theseequations express the second law of dynamics for translation alonglateral axis and rotation about the yaw axis. A critical step in themodeling process is computation of lateral forces of front and rearaxles. These forces are relational to the slip angles of tires: thelateral forces initially rise almost linearly with the slip angle, thencurve and saturate when the limit of adhesion is reached. The value oflateral forces at the limit is approximately proportional to thecoefficient of adhesion. Also the value of slip angle at saturation issmaller on slippery (low coefficient of adhesion) surfaces than on highcoefficient of adhesion surfaces. In order to capture these fundamentalproperties of lateral forces, they are modeled below at each axle bycombination of a parabolic segment with a straight line at the top as afunction of slip angle and the estimated coefficient of adhesion (FIG.15). An example is provided further below with reference to FIG. 4.

It can be shown that the following equations also hold true for thebicycle model of the vehicle:

dv _(y) /dt=a _(y) −v _(x)*Ω, and

a _(y)=(F _(yf) +F _(yr))/M.

The following observer is supported by the above equations (thesubscript “e” is added where estimations are used):

dv _(ye) /dt=−v _(x)*Ω_(a)+(F _(yfe) +F _(yre))/M+g ₁*(dΩ _(a) /dt−(a*F_(yfe) −b*F _(yre))/I _(zz))−g ₂*(dv _(ye) /dt−a _(y) +v _(x)*Ω_(a))−g₃*(a _(y)−(F _(yfe) +F _(yre))/M)

where F_(yfe) and F_(yre) used are estimates computed as describedbelow, Ω_(a) is the measured yaw rate and g₁, g₂ and g₃ are the observergains. If the estimates are perfect, then all expressions multiplied bythe gains vanish; however, when a discrepancy between the estimated andactual values arise, the terms multiplied by the gains provide feedbackto the vehicle model, reducing the errors between the actual andestimated values.

In the above observer, the first two terms comprise an open loop dynamicmodel of the vehicle responsive to the measured vehicle speed and themeasured yaw rate and the tire forces and the last three terms of theobserver comprise a closed loop component in which g₁ is multiplied by afirst error between the measured yaw rate and a predicted yaw rate, g₂is multiplied by a second error between a previously estimated lateralvelocity and a predicted lateral velocity and g₃ is multiplied by athird error between the measured lateral acceleration and apredictedlateral acceleration.

The above description does not take into account the effect of the bankangle of the road, which affects vehicle dynamics and the measuredlateral acceleration. Assuming a bank angle γ, a component of gravityforce, M*g*sin γ, is added to the balance of forces in the lateraldirection, yielding:

dv _(y) /dt=−v _(x)*Ω+(F _(yf) +F _(yr))/M+g*sin γ.

The difference between actual lateral acceleration a_(y) and measuredlateral acceleration a_(ym) is illustrated by:

a _(ym) =a _(y) −g*sin γ.

Since a_(y) is not measured and a_(ym) is, the feedback can be derivedfrom the following equation:

a _(ym)=(F _(yf) +F _(yr))/M,

which accounts for both level and banked road surfaces.

To reduce the tendency of the observer to develop steady-state error inresponse to a constant bank angle, the lateral acceleration error islow-pass filtered and the filter output is used as feedback in theobserver. Thus, the observer becomes:

dv _(ye) /dt=−v _(x)*Ω_(a)+(F _(yfe) +F _(yre))/M+g ₁*(dΩ _(a) /dt−(a*F_(yfe) −b*F _(yre))/I _(zz))−g ₂*(dv _(ye) /dt−a _(y) +v _(x)*Ω_(a))−g ₃*ΔA _(y) −g ₄ *ΔA _(yf),

where ΔA_(y) is [a_(y)−(F_(yfe)+F_(yre))/M] and ΔA_(yf) is the filteredversion of ΔA_(y). Thus now a fourth component of the closed loop errorterm is included as the low pass filtered result of the third error termto account for bank angle compensation.

In order to avoid differentiation of the yaw rate, the observer isrearranged using the following variable:

q=(1+g ₂)*v _(ye) −g ₁*Ω_(a),

so that the observer may be written in the form:

 dq/dt=−(1+g ₂)*v _(x)*Ω_(a)+((1+g ₃)/M−a*g ₁ /I _(zz))*F _(yfe)+((1+g₃)/M+b*g ₁ /I _(zz))F _(yre)+(g ₂ −g ₃)*a _(y) −g ₄ *ΔA _(yf).

The above equation is easily converted to discrete form and theestimates of lateral velocity and slip angle are obtained from thefollowing:

v _(ye)=(q+g ₁*Ω_(a))/(1+g ₂), and

tan β_(e) =v _(ye) /v _(x).

An example implementation of the above relationships is betterunderstood with reference now also to FIG. 4. Block 122 estimates theactual slip angle of the vehicle using the steering wheel angle signalon line 62, the actual measured vehicle yaw rate on line 81, the actualmeasured vehicle lateral acceleration on line 99, estimated vehiclespeed v_(x) on line 61 and the estimated lateral surface coefficient ofadhesion, μ_(L), on line 123. The slip angle estimation implements aniterative observer to determine the estimated vehicle slip angle, β_(e).The observer block 610 first estimates the side slip angles of front andrear axles using the following equations:

α_(fe) =[v _(ye)(k−1)+a*Ω _(a) ]/v _(x)−δ and

α_(re) =[v _(ye)(k−1)−b*Ω _(a) ]/v _(x),

where v_(ye)(k−1) is the estimated lateral velocity on line 622 from theprevious iteration of the observer, α_(fe) and α_(re) are the front andrear axle side slip angles provided on line 608.

The observer block 611 next estimates lateral forces of the front axle,F_(yfe) (FIG. 15), according to one of two functions 614 and 616,selected at block 612 as follows: $F_{yfe} = \left\{ \begin{matrix}{{{- c_{f}}*\alpha_{fe}*\left( {1 - {b_{cf}*{{\alpha_{fe}}/\mu_{L}}}} \right)},{{{if}\quad {\alpha_{fe}}} < {\mu_{L}*\alpha_{f^{*}}}}} \\{{{- N_{f^{*}}}*\left( {{\alpha_{fe}}/\alpha_{fe}} \right)*\left\lbrack {\mu_{L} + {s_{f}*\left( {{{\alpha_{fe}}/\alpha_{f^{*}}} - \mu_{L}} \right)}} \right\rbrack \quad {if}\quad {\alpha_{fe}}} \geq {\mu_{L}*\alpha_{f^{*}}}}\end{matrix} \right.$

where s_(f) is a small non-negative number (the slope of theF_(yf)−α_(f) curve at the limit of adhesion), e.g., s_(f)=0.05, andwhere α_(f*) is defined by:

α_(f*)=1/(2*b _(cf),)

where b_(cf) is defined by:

b _(cf) =c _(f)/(4*N _(f*)),

where

N _(f*) =M*b*(a _(ymax)+Δ_(a))/(a+b)

where a_(ymax) is the maximum lateral acceleration that the vehicle cansustain on a dry surface in m/s² and Δ_(a) is a constant, e.g.,Δ_(a)=0.5 m/s².

The observer block 611 similarly estimates lateral forces of the rearaxle, F_(yre), according to: $F_{yre} = \left\{ \begin{matrix}{{{- c_{r}}*\alpha_{re}*\left( {1 - {b_{cr}*{\alpha_{re}}}} \right)},{{{if}\quad {\alpha_{re}}} < {\mu_{L}*\alpha_{r^{*}}}}} \\{{{- N_{r^{*}}}*\left( {{\alpha_{re}}/\alpha_{re}} \right)*\left\lbrack {\mu_{L} + {s_{r}*\left( {{{\alpha_{re}}/\alpha_{r^{*}}} - \mu_{L}} \right)}} \right\rbrack},\quad {{{if}\quad {\alpha_{re}}} \geq {\mu_{L}*\alpha_{r^{*}}}}}\end{matrix} \right.$

where s_(r) is a small non-negative number, e.g., s_(r)=0.05 and whereα_(r*) is defined by:

α_(r*)=1/(2*b _(cr),)

where b_(cr) is defined as:

b _(cr) =c _(r)/(4*N _(r*)),

where

N _(r*) =M*a*(a _(ymax)+Δ_(a))/(a+b).

The observer block 620 then estimates a system state value, q(k),according to:

q(k)=q(k−1)+Δt*{−(1+g ₂)*v _(x)*Ω_(a)+((1+g ₃)/M−a*g ₁ /I _(zz))*F_(yfe)+((1+g ₃)/M+b*g ₁ /I _(zz))*F _(yre)+(g ₂ −g ₃)*a _(y) −g ₄ *ΔA_(yf)},

where ΔA_(y) is defined as:

ΔA_(y) =a _(y)−(F _(yfe) +F _(yre))/M,

and ΔA_(yf) is ΔA_(y) passed through a first order digital low passfilter, for example, with a cut off frequency of 1 rad/s.

Block 620 uses the state value, q(k), to determine estimates of lateralvelocity, v_(ye), and slip angle, β_(e), as follows:

v _(ye)(k)=(q(k)+g ₁*Ω_(a))/(1+g ₂) and

β_(e)=Arctan(v _(ye)(k)/v _(x)).

The gains g₁, g₂, g₃ and g₄ are tuning parameters preset by a systemdesigner, typically through routine experimentation on a test vehicle,and may vary from implementation to implementation. The estimated slipangle determined by block 122 is output on line 124.

Thus, as illustrated above, the control advantageously performs steps ofestimating a front side slip angle of front vehicle wheels (610),estimating a rear side slip angle of rear vehicle wheels (610),estimating a first lateral force of the front wheels on a road surfaceresponsive to the first side slip angle (611), estimating a secondlateral force of the rear wheels on the road surface responsive to thesecond side slip angle (611), wherein the first lateral force estimationis responsive to a first function (616) for low values of the front sideslip angle and responsive to a second function (614) for high values ofthe front side slip angle, wherein the second lateral force estimationis responsive to a third function (616) for low values of the rear sideslip angle and responsive to a fourth function (614) for high values ofthe rear side slip angle, estimating a vehicle lateral velocityresponsive to the first and second lateral force estimation andestimating a vehicle slip angle responsive to the vehicle lateralvelocity and a vehicle forward velocity (620).

The desired vehicle yaw rate, Ω_(d), and actual vehicle yaw rate, Ω_(a),are summed at block 134 to provide a yaw rate error signal on line 136,which is provided to the yaw rate command block 138. Similarly, thedesired vehicle slip angle, β_(d), and the estimated vehicle slip angle,β_(e), are summed at block 135 to provide a slip angle error signal online 137, which is provided to the slip angle command block 142.

Blocks 138 and 142 determine yaw rate and slip angle commands through aset of gains that are responsive to the vehicle speed signal on line 112and to the estimated surface coefficient of adhesion, μ_(e). Thecommands from blocks 138 and 142 are summed at block 146, which providesthe summation result, ΔM, on line 148 to block 154.

More particularly, the functions of blocks 134, 135, 138, 142 and 146may be explained as follows. A set of control gains are determined byfirst determining a value k′_(βp) according to:${k_{\beta \quad p}^{\prime}} = \left\{ \begin{matrix}{0,{{{if}\quad v_{x}} \leq v_{x1}}} \\{{{{- \left( {141.7 + {75/\mu_{e}}} \right)}*v_{x}} + \left( {1133.6 - {100/\mu_{e}}} \right)},{{{if}\quad v_{x1}} < v_{x} < 20},} \\{{{- 1700} - {1600/\mu_{e}}},{{{if}\quad v_{x}} \geq 20}}\end{matrix} \right.$

where

v _(xl)=(1133.6−100/μ_(e))/(141.7+75/μ_(e)).

The magnitude of the gain increases as μ_(e) decreases and increaseswith vehicle speed until it saturates at a predetermined vehicle speed,for example, at 20 rm/s. The gains are represented graphically in FIG. 5for three different surfaces, dry surface (reference 402) for whichμ≅1.0, snow (reference 404) for which μ≅0.4 and ice (reference 406) forwhich μ≅0.2. The gain calculation may be implemented as an equation orusing look-up tables providing the general shape shown in FIG. 5.

Next, a factor f₁ is determined according to:

f ₁=(k _(off) +k _(mult)*|β_(e)|/β_(max))²,

where k_(off) and k_(mult) are tuning parameters having example valuesof 1 and 0.5, respectively. The factor f₁ is then limited to a maximumvalue, for example, 4. As can be seen by the above equation, f₁,increases in value when the vehicle slip angle approaches or exceeds themaximum allowable limit. This function allows f₁ to regulate thetradeoff between control of yaw rate and control of slip angle. As thevehicle slip angle approaches the limit β_(max), which occurrences mayalso be characterized by a high slip angle error, the factor f₁increases the control influence or authority of the slip anglecorrection control as compared to the yaw rate correction control, thusproviding an advantageous tradeoff between yaw rate and slip anglecontrol. The increase in slip angle correction control authority isreflected in the proportional and derivative gains, k_(βp) and k_(βd),respectively, for the slip command, determined using f₁ as follows:

k _(βp) =c ₁ *f ₁ *k′ _(βp) and

k _(βd) ,=c _(βd) *k _(βp),

where c₁ is a tuning constant used to balance between slip angle controland yaw rate control and c_(βd) is the ratio between the differentialand proportional gains, e.g., c_(βd)=0.7.

The yaw rate proportional and derivative gains, k_(Ωp) and k_(Ωd), aredetermined as follows:

k _(Ωp) =f ₂ *k′ _(Ωp), and

k _(Ωd) =c _(Ωd) *k _(Ωp),

where c_(Ωd) is a constant (i.e., c_(Ωd)=0.4), where k′_(Ωp) is apreliminary gain that may either be constant or velocity dependent andwhere f₂ is a function of μ_(e), determined according to

f₂=1.25*((c ₂−0.2)+(1−c ₂)*μ_(e)),

where c₂ is a calibration constant, 0≦c₂<1, e.g., c₂=0.4. The aboveequations illustrate that the yaw rate gains, k_(Ωp) and k_(Ωd), areresponsive to f₂, which in turn is a function of the estimated surfacecoefficient of adhesion, μ_(e). The factor f₂ decreases as μ_(e)decreases, thus f₂ increases the yaw rate control gains on highcoefficient of adhesion surfaces (i.e., dry pavement) and decreases theyaw rate control gains on lower coefficient of adhesion surfaces (i.e.,ice). Like f₁, then, f₂ operates to regulate between yaw rate controland slip angle control, increasing yaw rate control authority on highcoefficient of adhesion road surfaces and decreasing yaw rate controlauthority on low coefficient of adhesion road surfaces.

The slip angle and yaw gains are used together with the actual anddesired slip angles and actual and desired yaw rates to determine thedesired corrective yaw moment, ΔM, for example, according to thefollowing equation:

ΔM=k _(βp)*(β_(d)−β_(e))+k _(βd)*(a _(y) /v _(x)−Ω_(a))+k_(Ωp)*(Ω_(d)−Ω_(a))+k _(Ωd)*(Ω_(du)′−Ω_(a)′)

where Ω_(du)′ and Ω_(a)′ are the time derivatives of Ω_(du) and Ω_(a),determined, for example, by passing each signal through a high passfilter. The value (a_(y)/v_(x)−Ω_(a)) may be passed through a high pass“wash-out” filter, for example, having a transfer function of s/(s+1),in order to reduce the effects of sensor bias and banking of the road.

In the above equation for ΔM, the first two terms represent the slipangle command and the third and fourth terms represent the yaw ratecommand. The desired corrective yaw moment command, ΔM, is output fromblock 146 to the output command block 154.

In one example, the first term of the above equation for ΔM may beignored. In that case the slip angle command is limited to control basedon slip rate, since β′≈a_(y)/v_(x)−Ω_(a), This simplifies the algorithmsince slip angle β does not have to be estimated and the desired valueof slip angle is not used. The control gain k_(βd) is computed asdescribed above, i.e., it varies with vehicle speed and with the surfacecoefficient of adhesion but with the factor f₁ set equal to 1.0.

In another example, the term (a_(y)/v_(x)−Ω_(a)) may be replaced with acalculation of the slip angle error derivative Δβ′ determined asfollows:

Δβ′=(β_(e)(k)−β_(du)(k)−(β_(e)(k−1)−β_(du)(k−1)))/Δt,

and then filtered through a low pass filter having a bandwidth of about26 Hz.

In another example, the first two terms of the equation for ΔM are setto zero when a magnitude of the sum of the first two terms otherwise isnot above a predetermined value, defining a dead zone below which slipangle control is not triggered. The predetermined value defining thedead zone is set as desired by the system designer.

Before the output command block 154 makes use of the corrective yawmoment command, it must first determine whether the vehicle is in anoversteer or understeer condition. An understeer condition isestablished if the sign of ΔM and the steer angle δ are the same. If δand ΔM have opposite signs, i.e., the product of δ and ΔM is less thanzero, or if either of the values is equal to zero, then the vehicle isdesignated as being in oversteer mode.

In order to avoid frequent changes in the oversteer/understeerdesignation due to sensor noise when either δ or ΔM are close to zero, adead zone is introduced. That is, the vehicle is designated as being inoversteer when the product of δ and ΔM is less than or equal to zero.The vehicle is designated as being in understeer when the product of δand ΔM is greater than THRESHD, where THRESHD is a dead zone thresholddetermined by the system designer. When the product of δ and ΔM isgreater than zero but not greater than THRESHD, the most recentunder/oversteer designation is maintained.

The corrective yaw force command, F, is determined by dividing ΔM byhalf of the vehicle's track width, d.

Applying the yaw force command to the actuators first involvesdistributing the force command to the various wheel brakes of thevehicle. As used herein, the designation of inside and outside are withrespect to the direction of turn. If the vehicle is being steered right,then the right front and right rear wheels are the inside wheels and theleft front and rear wheels are the outside wheels. If the vehicle isbeing steered left, then the left front and rear wheels are the insidewheels and the right front and rear wheels are the outside wheels. Thedistribution of the commanded yaw force to the wheels described below isjust one specific example of distribution, other examples are describedin pending U.S. patent applications, Ser. No. 08/654,982 and Ser. No.08/732,582, both assigned to the assignee of this invention.

If there is no driver commanded braking of the vehicle, i.e., if thebrake pedal of the vehicle is not depressed as sensed by the brake pedalswitch, then the distribution control is as follows. In an understeercondition, braking is applied in approximately equal distribution (theexact distribution may depend on a particular vehicle) to the insiderear and inside front wheels up to the point where ABS for the front andrear wheels is activated. At that point, the braking force applied tothe wheels is not increased. If the rear wheel enters ABS control beforethe desired braking force is developed, the portion of the brake commandsent to the inside rear wheel that the inside rear wheel was not able toachieve before entering ABS control is sent to the front inside wheel.The exception to this general control is in the case when the estimatedlateral force of the rear axle, F_(yr), and steering angle have oppositesigns. In this case, the distribution is front biased, for example, 10%of the desired force to the inside rear wheel and 90% of the desiredforce to the inside front wheel. In the case of a two-channel system,the entire yaw force is applied to the inside front wheel.

In oversteer when the driver is not commanding braking, the brakes areapplied to the outside front wheel only and braking force may be allowedto exceed the ABS limit. That is, the ABS control is overridden and thefront wheel may be allowed to rise to higher slip levels and even toachieve a lock-up condition that the ABS control would normally prevent.The ABS control is overridden when the following conditions aresimultaneously met: ABS control is active; the signs of estimatedlateral force of the front axle, F_(yf), and steering angle are thesame; the vehicle is and has been in oversteer condition for at least0.1 seconds; and the total desired braking force of a particular wheel,F_(xd), is and has been for at least 0.1 seconds at least 1.5 timeslarger than the estimated braking force at the ABS limit, F_(xlim).F_(xd) is determined by summing, for a particular wheel, the estimatedbrake force requested by the vehicle driver and the brake forceresulting from the yaw force command. The forces F_(xlim) for the frontleft and right wheels are computed as follows:$F_{xliml} = \left\{ {{\begin{matrix}{{N_{lf}*\mu_{e}\quad {if}\quad {\alpha_{f}}} \leq {0.017*\left( {1 + \mu_{e}} \right)}} \\{{{\min \left( {{N_{lf}*\mu_{e}};{N_{lf}*\mu_{e}^{2}*{\lambda_{\max}/{\alpha_{f}}}}} \right)}\quad {if}\quad {\alpha_{f}}} > {0.017*\left( {1 + \mu_{e}} \right)}}\end{matrix}F_{xlimr}} = \left\{ \begin{matrix}{{N_{rf}*\mu_{e}\quad {if}\quad {\alpha_{r}}} \leq {0.017*\left( {1 + \mu_{e}} \right)}} \\{{{\min \left( {{N_{rf}*\mu_{e}};{N_{rf}*\mu_{e}^{2}*{\lambda_{\max}/{\alpha_{r}}}}} \right)}\quad {if}\quad {\alpha_{r}}} > {0.017*\left( {1 + \mu_{e}} \right)}}\end{matrix} \right.} \right.$

where λ_(max) is the maximum brake slip at the ABS limit, e.g.,λ_(max)=0.1, and N_(lf) and N_(rf) are the estimated normal tire forceson the left and right front wheels, respectively, defined by:

N _(lf) =M*g*b/(2*(a+b))+K _(rllf) *M*h*a _(y) /trw; and

N _(rf) =M*g*b/(2*(a+b))−K _(rllf) *M*h*a _(y) /trw,

where K_(rllf) is the fraction of total roll stiffness developed by thefront suspension (e.g., K_(rllf)=0.6), trw is the average of the frontand rear track widths and h is the height of the vehicle center ofgravity above the roll axis.

If there is driver commanded braking, the understeer condition iscontrolled as described above for the no driver-commanded braking mode,except that when both of the inside wheels (inside front wheel in a twochannel system) reach an ABS limit before the total desired force isgenerated, then the brake command of the outside front wheel is reduced.The amount of brake command reduction to the outside front wheel is anamount necessary to transfer to the vehicle the difference between theyaw force command and the yaw force achieved by the two inside wheelsbefore they went into ABS, except that the brake command reduction tothe outside front wheel is limited so that at least a fixed percentage(e.g., 50%) of the driver commanded braking to the outside front wheelis maintained.

In the oversteer condition while there is driver commanded braking, theyaw force command is first applied to the outside front wheel brake,increasing brake force, possibly including to a point allowing the wheelto override the ABS limit. If the force achieved by the outside frontwheel is not sufficient to produce the desired corrective yaw moment onthe vehicle, braking of the inside rear wheel may be reduced by up to50% of the driver commanded braking force for that wheel and if theforce achieved by the outside front wheel and inside rear wheel (outsidefront only for a two channel system) is still not sufficient, thenbraking of the inside front wheel may be reduced by up to 50% of thedriver commanded braking force for that wheel. When the ABS isoverridden, the locking of the outside front wheel reduces the lateralforce of the front wheel, which reduction of lateral force may be takeninto account when calculating the corrective yaw moment.

Once the force commands are determined, they may be applied to theactuators as represented by line 158 and block 132. In this control, itis necessary to reasonably estimate the amount of brake force applied ateach particular wheel to determine the portion of the corrective yawmoment achieved by that wheel. There are many known ways of determiningbrake force in an individual wheel. In one example, hydraulic fluidpressure sensors in the individual wheel brake lines sense the amount ofhydraulic pressure in the individual wheel brakes, and that sensedhydraulic pressure corresponds to a brake force measurement. In vehicleswhere the brake actuators are motor driven reciprocating piston devices,the brake force may be determined by either position control or motorcurrent feedback of the actuators, which position and/or motor currentsignals are taken as measurements of brake force at the individualwheels. Any other known method for measuring brake force at theindividual wheels may be used and provided as feedback as represented byline 152 to the output command block 154, for example to implementclosed loop proportional derivative control of the actuators representedby block 132.

In vehicles where there is no means to provide a feedback of actualbrake force through a brake actuator or pressure transducer, individualwheel speed control may be used to implement the brake force command inthe vehicle wheel brakes. In one example, the desired yaw force, F, maybe converted into a wheel speed difference command (commanding a speeddifference between left and right wheels) as follows:

Δv _(xo) =F*g _(v1) *g _(v2),

where g_(v1) is a first gain value that varies linearly with vehiclespeed and g_(v2) is a second gain value that varies non-linearly withthe estimated surface coefficient of adhesion. An example graph of g₂ isshown in FIG. 6.

In another example, the desired wheel speed difference, Δv_(xo), isrelated directly to the slip angle errors and yaw rate errors withoutthe intermediate step of calculating the desired yaw force. In thatcase:

Δv _(xo) =[k _(βp)*(β_(d)−β_(e))+k _(βd)*(a _(y) /v _(x)−Ω_(a))+k_(Ωp)*(Ω_(d)−Ω_(a))+k _(Ωd)*(Ω_(du)′−Ω_(a)′)]*v _(x),

where the control gains k_(βp), k_(βd), k_(Ωp) and k_(Ωd) are determinedin the same manner as described above in connection with ΔM, except thatk′_(βp) and k′_(Ωp) are determined as follows. The preliminaryproportional gain k′_(Ωp) is constant or speed dependent. Thepreliminary slip angle gain k′_(βp) is determined (e.g., by usinglook-up tables) as a function of the estimated surface coefficient ofadhesion, μ_(e), and vehicle speed, v_(x). An example of relationshipsbetween k′_(βp) and vehicle speed on three different road surfaces areshown in FIG. 7. Reference 420 illustrates the relationship for a dryroad surface having μ≅1.0. Reference 422 illustrates the relationshipfor a snowy road surface having μ≅0.4 and reference 424 illustrates therelationship for an icy road surface having μ≅0.2. For intermediatecoefficients of adhesion, linear interpolation may be used.

The wheel speed difference actually applied to the wheels, Δv_(x), isdetermined by Δv_(xo) and the kinematics of the turn, i.e.,

Δv _(x) =Δv _(xo)+Ω_(a) *trw,

where trw is the track width (for the axle to which Δv_(x) is applied).

The wheel speed difference command, Δv_(x), is distributed to thevehicle wheels as the yaw force command is distributed above. Forexample, in the understeer condition when no driver braking is applied,half of Δv_(x) is applied to the inside rear wheel and half Δv_(x) isapplied to the inside front wheel to reduce the inside rear wheel speedby 0.5*Δv_(x) less than its original speed prior to activation of theyaw control and to reduce the inside front wheel speed by 0.5*Δv_(x)less than its original speed prior to activation of the yaw control. Ifthe rear wheel enters ABS then the front wheel is slowed by an amountΔv_(xf) equal to Δv_(x) minus Δv_(xr), where Δv_(xr) is the amount ofinside rear wheel speed reduction achieved prior to the inside rearwheel entering ABS.

The wheel speed control is similarly applied for the other brakingdistributions described above. Thus closed loop wheel speed control maybe used to transfer the desired corrective yaw force, F, capable ofachieving the desired corrective yaw moment, ΔM, to the vehicle body.

The commands determined at block 154 are only applied to the vehiclewheel brakes if the entry conditions for the active brake control areestablished and then are only applied until the exit conditions foractive brake control are established. First the estimated vehicle speedmust be above a certain speed of entry, v_(min), which is typically low,for example 5 miles per hour. If this condition is satisfied, then thesystem becomes active when either yaw rate error exceeds a yaw rateerror threshold or when the corrective yaw moment, ΔM, exceeds acorrective yaw moment threshold (or when wheel speed difference, Δv_(x),exceeds a threshold). The yaw rate error test may be implemented by:

|Ω_(d) Ω+k _(e)*(Ω_(du)′−Ω_(a)′)|>Ω_(thresh),

where Ω_(du)′ and Ω_(a)′ may be determined by passing Ω_(du) and Ω_(a)through high pass filters to time differentiate them, k_(e) is a fixedconstant and Ω_(thresh) is determined in response to vehicle speed andsteering wheel angle. In one example, Ω_(thresh) is determined asfollows:

Ω_(thresh)=(9−0.036*v _(x)+1.3*(v _(x)δ)/((a+b)+K _(u) *v _(x) ²))/57.3,

if the vehicle is in understeer mode, and as:

Ω_(thresh)=(7+1.3*(v _(x)*δ)/((a+b)+K _(u) *v _(x) ²))/57.3,

if the vehicle is in oversteer mode. In the above equations, Ω_(thresh)is expressed in (rad/s), v_(x) is expressed in (m/s), δ is expressed in(rad), a and b are expressed in (m) and K_(u) is the vehicle understeercoefficient.

An exit condition is established if the total corrective yaw momentdrops below a predetermined threshold value and remains below that valuefor a predetermined period of time or if the yaw rate error is below apredetermined yaw rate error threshold for a predetermined period oftime. If either of these conditions exists, the output command block 154is disabled and prevented from providing output commands to actuators132 to establish corrective yaw moments on the vehicle. An exitcondition is also established regardless of the above conditions if thevehicle speed drops below the speed of exit.

Referring now to FIG. 8, an example main flow control routineillustrating example steps performed by a controller for achieving thedesired yaw rate and slip angle control herein is illustrated. At block250 the system receives the inputs from the various system sensors andthen at block 252 the vehicle determines the desired vehicle states asdescribed above with reference to block 102 in FIG. 3. Block 254estimates the lateral coefficient of adhesion between the vehicle tiresand the road surface as described above with reference to block 120 inFIG. 3. At block 256, the routine estimates the actual vehicle slipangle as described above with reference to block 122 in FIG. 3. Block258 then determines the control gains for the slip and yaw rate commandsas described above with reference to blocks 138 and 142 in FIG. 3. Block260 then determines the corrective yaw moment command, ΔM, (or thedesired wheel speed difference, Δv_(x)) as described above withreference to block 154 in FIG. 3 and block 262 performs the enter/exitcontrol determination. If the enter/exit control block 262 enablesactuator control, then the actuator commands are determined at block 264and output at block 266 to the various vehicle wheel brake actuators toachieve the desired corrective yaw moment on the vehicle body tominimize yaw rate error and vehicle slip angle error.

Referring now to FIG. 9, the steps for determining the desired vehiclestates at block 252 (FIG. 8) are shown. At block 268, the vehicle modeldescribed above with reference to block 102 in FIG. 3 is used todetermine v_(yd), Ω_(du), a_(yd), and β_(du). Next, block 270 uses theestimated surface coefficient of adhesion and the steering wheel angleto determine β_(max), which is used with β_(du) to determine β_(d) atblock 272. Block 274 determines Ω_(d). All of the steps, 268, 270, 272and 274 may be implemented as described above with reference to FIG. 3,block 102.

FIG. 10 illustrates the steps performed by block 258 in FIG. 8 fordetermining the control gains for the yaw rate command and slip anglecommand. More particularly, block 276 determines the preliminaryproportional gain, k′_(βp), as a function of v_(x) and μ_(e) and block278 determines the slip angle gain factor, f₁, as a function of β_(e)and β_(max). Then block 280 determines the slip angle gains as afunction of k′_(βp) and f₁. Block 282 determines the yaw rateproportional and derivative gains as a function of μ_(e). The steps atblocks 276, 278, 280 and 282 may be implemented as described above withreference to blocks 138 and 142 in FIG. 3.

Referring now to FIG. 11, the steps performed by the enter/exit controlblock 262 in FIG. 8 are shown. First at block 302, the forward vehiclevelocity, v_(x), is compared to a minimum velocity. If v_(x) is notgreater than the minimum vehicle velocity, the routine continues toblock 320 where a flag is set, disabling the active brake control. Ifv_(x) is greater than the minimum vehicle velocity, the routinecontinues to block 304 where it determines Ω_(thresh), as describedabove with reference to block 154 in FIG. 3. If Ω_(err) is greater thanΩ_(thresh) at block 306, then the routine continues to block 310.Otherwise, the routine continues to block 308 where it compares themagnitude of the command ΔM to a threshold moment value. If ΔM does nothave a magnitude greater than the threshold moment value, then theroutine continues to block 312. Otherwise, the routine continues toblock 310, where a flag is set enabling control of the brake systemthrough the active brake control.

At blocks 312 and 313, the absolute values of ΔM(Δv_(x)) and Ω_(err) arecompared to the exit threshold values. If either ΔM(Δv_(x)) or Ω_(err)is less than the exit threshold values, the routine continues to block314 where a timer is incremented. Otherwise, at block 316, the timer isreset. Block 318 compares the timer to a time out value. If the timer isgreater than the time out value, the routine continues to block 320where the flag is set disabling active brake control. Otherwise, theenter/exit control 262 is exited.

Another example of entry/exit conditions is set forth in pending U.S.patent application, Ser. No. 08/732,582.

Referring now to FIG. 12, example steps performed by the actuatorcommand block 264 in FIG. 8 are shown. First block 350 checks theundersteer flag that, as described above with reference to block 154 inFIG. 3, indicates whether or not the vehicle is experiencing understeeror oversteer. If the understeer flag is set, the routine continues toblock 352 where it compares the signs of the estimated lateral force atthe rear axle, F_(yr), and the vehicle steering wheel angle. If they aredifferent, for example, when the product F_(yr)*δ is less than zero,then the routine continues to block 356 where it sets the rear insidewheel force command F_(ir) equal to 0.1*F. If at block 352, F_(yr)*δ isnot less than zero, then block 354 sets F_(ir) equal to 0.5*F. Thisportion of the algorithm is used only for a four channel system.

From blocks 354 or 356, the routine continues to block 358 where itchecks whether or not the inside rear wheel is in ABS mode. If so, block360 determines the actual force applied by the inside rear wheel when itentered ABS, F_(ira), and block 364 determines the inside front wheelforce command, F_(if), equal to F minus F_(ira). If, at block 358, therear wheel is not in ABS, then block 362 sets the inside front wheelcommand equal to F−F_(ir) Then at block 366, the routine checks whetheror not braking is commanded by the vehicle driver, for example, bydetermining whether or not there is an output signal from the brakepedal switch or from the master cylinder pressure transducer. If not,the subroutine 264 exits. Otherwise, the routine continues to block 368where it checks whether or not the inside front and rear wheels are inABS. If so, block 370 determines the actual force achieved by the insidefront and rear wheels, F_(ifa) and F_(ira), and then block 372determines an outside front wheel brake force command, F_(of), equal toF−F_(ifa)−F_(ira). Block 374 limits the command F_(of) to a valuebetween zero and half of the driver commanded brake force of the outsidefront wheel. From block 374 the routine is exited.

If at block 350 the routine is not in understeer mode, then it proceedsto the oversteer steps at block 376 where the outside front wheel forcecommand, F_(of), is set equal to F. Then block 378 checks whether or notbraking is commanded. If not, block 380 sets a flag inhibitingactivation of ABS control of the outside front wheel so that the outsidefront wheel is allowed to lock if the command, F_(of), so commands (theconditions under which the wheel is allowed to lock were specifiedabove). From block 380, the subroutine 264 is exited.

If at block 378 there is driver commanded braking, the routine continuesto block 382 where it checks whether the outside front wheel is in ABS.If not, the subroutine 264 is exited. If so, the subroutine continues toblock 384 where it determines the actual braking force achieved by theoutside front wheel, F_(ofa). The routine then moves to block 386 wherean inside front wheel brake force command, F_(if), is determined equalto F−F_(ofa). If the outside front wheel is allowed to lock, then theeffect of reduction in lateral force on the vehicle yaw moment isincluded in the above calculation; this yields:

F _(if) =F−F _(ofa)−μ_(e) *N _(of) *a*2/trw,

where N_(of) is the normal force on the outside front wheel determinedas described above with reference to the lock-up conditions. The insidefront wheel brake force command is then limited to half thedriver-commanded braking to that wheel, as determined by the driver'sbrake request at block 388. Block 390 then determines the inside rearwheel brake force command as the difference between the commanded yawforce, F, and the yaw forces achieved by the outside and inside frontwheels. At block 392, the inside rear wheel brake force is limited to nogreater than one half the driver commanded braking to the inside rearwheel.

It is noted that in the oversteer mode when there is driver braking, thefront and rear inside wheel brake force commands, F_(if) and F_(ir),command reduction in the braking force at the front and rear insidewheels. Similarly, in the understeer mode when there is driver braking,the outside front wheel brake command, F_(of), commands a reduction inthe braking force applied to the outside front wheel.

For vehicles with no means to provide feedback of actual brake forcethrough a brake actuator or pressure transducer, the same logic fordistributing the command signal among the wheels applies with the brakeforces replaced by the corresponding changes in wheel velocities.

FIG. 13 illustrates another example vehicle reference model fordetermining desired yaw rate, Ω_(d), and desired slip angle, β_(d). Thevehicle reference model 448 shown includes a single filter 450, fourlook up tables (or equations) 452, 454, 462 and 464 and three simpleequation functions 456, 458 and 460. The filter 450 implements thedesired vehicle dynamics as represented by the damping ratio and naturalfrequency in a single filter whose output is used by the relativelysimple calculations in blocks 456, 458 and 460 to calculate both thedesired slip angle and desired yaw rate.

More particularly, the damping ratio and natural frequency may beexpressed according to the system parameters as follows:

ω_(n)=(a ₁₁ *a ₂₂ −a ₁₂ *a ₂₁)^(½) and

ζ=−(a ₁₁ +a ₂₂)/(2*(a ₁₁ *a ₂₂ −a ₁₂ *a ₂₁)^(½)),

or in any reasonably desired values which vary with speed and which canbe programmed into controller memory as look-up tables 462 and 464responsive to the vehicle speed input v_(x) or implemented ascalculations.

Using ω_(n) and ζ and the steering wheel angle input δ, the filter 450performs a filter function as follows:

x ₁′=δ−2*ω_(n) *x ₁−ω_(n) ² *x ₂

x ₂ ′=x ₁

with the filter result provided to blocks 456 and 460. Block 456 alsoreceives the slip angle gain output of block 452, which is a threedimensional look up table implementing the following function:

V _(ydssgain)=(δ*v _(x)/((a+b)+K _(u) *v _(x) ²))*(b−(a*M*v _(x)²)/((a+b)*c _(r)).

Using V_(ydssgain), ω_(n) and the output of filter 450, block 456determines the desired lateral velocity v_(yd), according to:

v _(yd) =b ₁ *x ₁ +V _(ydssgain)*ω_(n) ² *x ₂.

Block 458 then determines β_(du) according to:

β_(du)=tan⁻¹(v _(yd) /v _(x)).

Block 454 is a look up table determining the yaw rate gain according tothe function:

R _(gain)=(δ*v _(x)/((a+b)+K _(u) *v _(x) ²))

Using R_(gain), ω_(n) and the output of filter 450, block 460 determinesthe desired yaw rate Ω_(d), according to:

Ω_(d) =b ₂ *x ₁ +R _(gain)*ω_(n) ² *x ₂.

Using the above approach allows the system designer to (a) select thedamping ratio and natural frequency desired of the vehicle referencemodel, (b) define a single filter representing the selected dampingratio and natural frequency, (c) apply steering angle to the filter, (d)use the filter output with a predetermined slip angle gain function todetermine desired vehicle slip angle and (e) use the filter output witha predetermined yaw gain function to determine the desired vehicle yawrate.

FIG. 14 illustrates another example vehicle reference model using asingle filter. The vehicle reference model 558 includes the singlefilter 550, look up tables 552, 554, 562 and 564 and functions 556, 558and 560. The look up tables 562, 564 and 554 are the same as look uptables 462, 464 and 454 shown in FIG. 13. Similarly, the function blocks558 and 560 are the same as function blocks 458 and 460 in FIG. 13.

Filter 550 is implemented in discrete form according to:

x ₁(k+1)=c ₁ *x ₁(k)+c ₂ *x ₂(k)+c ₃ *V _(ydss)(k+1), and

x ₂(k+1)=x ₂(k)+T*x ₁(k),

where

c ₁=1(1+2*ζ*ω_(n) *T),

c ₂=ω_(n) ² *c ₃, and

c ₃ =T*c ₁,

where T is the sampling period, and where

V _(ydss)(k+1)=(δ*v _(x)(k)/((a+b)+K _(u) *v _(x)(k)²))*(b−(a*M*v_(x)(k)²)/((a+b)*c _(r)).

The output of filter 550 is used by block 556 to compute the desiredlateral velocity, v_(yd)(k+1), according to:

v _(yd)(k+1)=ω_(n) ²*(x ₂(k+1)+x ₁(k+1)/z),

where z=a₁₂*b₂/b₁−a₂₂. The computation at block 556 is performed in atwo-step process. First the value of z is computed and, if z equalszero, then z is limited to a predetermined minimum magnitude.

What is claimed is:
 1. A brake system control method, comprising thesteps of: measuring a set of vehicle parameters including steering wheelangle, vehicle speed, lateral acceleration and vehicle yaw rate;responsive to the measured parameters using an observer to estimatelateral velocity of the vehicle, wherein the observer contains (a) anopen loop nonlinear dynamic model of the vehicle responsive to themeasured vehicle speed and the measured yaw rate; (b) a closed loop termresponsive to a first error between the measured yaw rate and apredicted yaw rate, a second error between a previously estimatedderivative of lateral velocity and a predicted derivative of lateralvelocity and a third error between the measured lateral acceleration anda predicted lateral acceleration; estimating a vehicle slip angleresponsive to the estimate of lateral velocity; determining a controlcommand responsive to the vehicle slip angle; and controlling anactuator responsive to the control command.
 2. A brake system controlmethod according to claim 1, wherein the closed loop term of theobserver is also responsive to a fourth error determined by low-passfiltering the third error, wherein the measured lateral acceleration ismeasured in a direction lateral to a body of the vehicle and whereinbank angles of the road surface are compensated for.
 3. A brake systemcontrol method according to claim 1, also comprising the step of:responsive to the measured parameters, estimating a coefficient ofadhesion between vehicle wheels and a road surface, wherein the openloop nonlinear dynamic model of the vehicle is also responsive to theestimated coefficient of adhesion.
 4. A brake system control methodcomprising the steps of: estimating a front side slip angle of frontvehicle wheels; estimating a rear side slip angle of rear vehiclewheels; estimating a first lateral force of the front wheels on a roadsurface responsive to the first side slip angle; estimating a secondlateral force of the rear wheels on the road surface responsive to thesecond side slip angle, wherein the first lateral force estimation isresponsive to a first function for low values of the front side slipangle and responsive to a second function for high values of the frontside slip angle, wherein the second lateral force estimation isresponsive to a third function for low values of the rear side slipangle and responsive to a fourth function for high values of the rearside slip angle, wherein the first and third functions are similar to aparabolic segment and wherein the second and fourth functions include astraight line; estimating a vehicle lateral velocity responsive to thefirst and second lateral force estimation; estimating a vehicle slipangle responsive to the vehicle lateral velocity and a vehicle forwardvelocity; determining a control command responsive to the estimatedvehicle slip angle; and controlling a chassis system actuator responsiveto the control command.
 5. A brake system control method according toclaim 4, wherein the first lateral force estimation is responsive to thefirst function when a first product of the first side slip angle and anestimate of surface coefficient of adhesion is below a first thresholdand responsive to the second function when the first product is notbelow the first threshold, and the second lateral force estimation isresponsive to the second function when a second product of the secondside slip angle and the estimate of surface coefficient of adhesion isbelow a second threshold and responsive to the fourth function when thesecond product is not below the second threshold.